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Linear Programming — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsLinear Programming1 Mark
MCQ
A linear programming problem is as follows:
Minimize $Z=30 x+50 y$
Subject to the constraints,
$\begin{array}{l}3 x+5 y \geq 15 \\ 2 x+3 y \leq 18 \\ x \geq 0, y \geq 0\end{array}$
In the feasible region, the minimum value of $Z$ occurs at
  • A
    a unique point
  • B
    no point
  • C
    infinitely many points
  • D
    two points only
✓

Answer

Here, the feasible region is shaded.
Image
Corner pointsValue of Z=30 x+50 y
A(0,3)30 xx0+50 xx3=150 (Minimum)
B(5,0)30 xx5+50 xx0=150quad (Minimum)
C(9,0)30 xx9+50 xx0=270
D(0,6)30 xx0+50 xx6=300
Since, minimum value of $Z$ occurs at both $A$ and $B$. So, $Z$ is minimum at every point on the line joining $A B$. So, minimum value of Z occurs at infinitely many points.

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